Currently the hydrological model only includes a description of a channelized drainage system (i.e., a single channel). In reality ice sheet/glacier beds will also have a spatially distributed drainage system that co-exists with the channel(s).
You could add a description of a distributed drainage system to the model. This would be a useful addition because basal sliding is probably controlled by the pressure in the distributed system and because, at least in the case of a linked-cavity system, the drainage system size evolves as a function of sliding, e.g., Kingslake et al., 2013.
Two ways to do this: 1. (simpler) follow (Schoof 2010) [https://www.nature.com/articles/nature09618] and add an opening term to the channel equation, u.R, where R is a prescribed bed obstacle size. This lumps together the channelized drainage system with the distributed system into one description. The physical interpretation of this is a little vague, if you ask me.
(more complicated) follow Kingslake et al., 2013 and introduce a whole set of equations which exist in parallel to the channelized system and exchanges water with it. A weakness of that paper is that it assumes a pseudo steady state in the distributed drainage system. An improvement would be to remove this assumption.
Both of the these approaches are less then ideal and will require some thought, and I suggest not moving on to this immediately, but leaving it for the future for now.
Currently the hydrological model only includes a description of a channelized drainage system (i.e., a single channel). In reality ice sheet/glacier beds will also have a spatially distributed drainage system that co-exists with the channel(s).
You could add a description of a distributed drainage system to the model. This would be a useful addition because basal sliding is probably controlled by the pressure in the distributed system and because, at least in the case of a linked-cavity system, the drainage system size evolves as a function of sliding, e.g., Kingslake et al., 2013.
Two ways to do this: 1. (simpler) follow (Schoof 2010) [https://www.nature.com/articles/nature09618] and add an opening term to the channel equation, u.R, where R is a prescribed bed obstacle size. This lumps together the channelized drainage system with the distributed system into one description. The physical interpretation of this is a little vague, if you ask me.
Both of the these approaches are less then ideal and will require some thought, and I suggest not moving on to this immediately, but leaving it for the future for now.